Yep, digging and glyphosate. Cut back, expose the mother plant's roots, dig out as much as you can. It will be hard work. Scrape or cut remaining roots to expose bare wood and paint on glyphosate rather than spray it.

Make sure you stick to the recommended dosage. There's always a temptation to strengthen the mixture on the basis that it will work better. It won't. It will only kill that localised area and not work through the plant's system. You will probably need several glyphosate treatments.

Apart from dealing with the mother plant, you have to deal individually with any outcrops which will have rooted themselves separately from the mother plant.